In the past, electroluminescent display devices (hereinafter simply referred to as EL display devices) have been known including EL display devices of a double insulating layer type in which the sides of an electroluminescent light-emitting layer (hereinafter simply referred to as an EL layer) are held between insulating layers which are in turn held externally between a transparent electrode made essentially of indium oxide (In.sub.2 O.sub.3) or tin oxide (SnO.sub.2) and a metal electrode made of aluminium (Al) or the like and EL display devices of a single insulating layer type in which an EL layer is directly formed on a transparent electrode mass essentially of indium oxide or tin oxide and then an insulating layer and a metal electrode are successively provided on the EL layer. If these two types of EL display devices are constructed so that they have the same total insulating layer thickness and the same EL emitting thickness and an ac voltage or pulse voltage is applied to cause light emission, the EL display device of the single insulating layer type is lower than the EL display device of the double insulating layer type in terms of luminescent threshold voltage and also the EL display device of the double insulating layer type is higher than the EL display device of the single insulating layer type in terms of luminescent brightness. Thus, the known EL display devices have had their own merits and demerits and therefore there has been a demand for an EL display device which has a lower luminescence threshold voltage or is adapted to be driven at a lower voltage and which also has a higher luminescent brightness.